PROPERTIES OF A BURSTING MODEL WITH 2 SLOW INHIBITORY VARIABLES

Models for certain excitable cells, such as the pancreatic beta-cell, must reproduce ''bursting'' oscillations of the membrane potential. Th is has previously been done using one slow variable to drive bursts. T he dynamics of such models have been analyzed. However, new models for the beta-cell often include additional slow variables, and therefore the previous analysis is extended to two slow variables, using a simpl ified version of a beta-cell model. Some unusual time courses of this model motivated a geometric singular perturbation analysis and the app lication of averaging to reduce the dynamics to the slow-variable phas e plane. A geometric understanding of the solution structure and of tr ansitions between various modes of behavior was then developed. A nove l use of the bifurcation code AUTO finds nullclines for the slow varia bles when the fast variables are periodic by averaging over the fast o scillations. In contrast with the ''parabolic'' neuronal burster, this model requires bistability in the fast variables to generate bursting .